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Equity Risk Premium Predictability from Cross-Sectoral Downturns*

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Equity Risk Premium Predictability from Cross-Sectoral Downturns* Equity Risk Premium Predictability from Cross-Sectoral Downturns* José Afonso Faias and Juan Arismendi Zambrano This version: July 2017 Abstract We illustrate the role of left tail mean (LTM) in equity risk premium (ERP) predictability. LTM measures the average of pairwise left tail dependency among major equity sectors incorporating endogenous shocks that are imperceptible at the aggregate level. LTM, as the variance risk premium, significantly predicts the ERP in- and out-of- sample, which is not the case with the other commonly used predictors. Ceteris paribus, an increase of two standard deviations in the LTM in a time-varying disaster-risk consumption-based asset pricing model causes an increase of 0.70% in the ERP. This paper contributes to the debate on ERP predictability. Keywords: Predictability, left tail dependence, asset pricing model. JEL classification: G10, G12, G14. *Corresponding author: José Afonso Faias, UCP - Católica Lisbon School of Business & Economics, Palma de Cima, 1649-023 Lisboa, Portugal. Phone +351-217270250. E-mail: [email protected]. Juan Arismendi Zambrano, Department of Economics, Finance and Accounting, Maynooth University -National University of Ireland, Maynooth, Ireland. Phone +353-(0)1- 7083728. E-mail: [email protected]; ICMA Centre – Henley Business School, University of Reading, Whiteknights, RG6 6BA, Reading, UK. Phone +44-1183788239. E-mail: [email protected]. We thank Rui Albuquerque, Gregory Connor, Adam Farago, Campbell Harvey, Joni Kokkonen, Stefan Nagel, Pedro Santa-Clara, Kenneth J. Singleton, Grigory Vilkov, Andrew Vivian, Jessica A. Wachter, and the participants at the 2016 FMA Annual Meeting, 2016 Research in Options, 2017 FMA European Conference, 2017 Multinational Finance Society Annual Meeting, 2017 European Finance Association Annual Meeting, and the 2017 Foro Finanzas for helpful comments and discussions. We are particularly grateful to João Monteiro, Pavel Onyshchenko and Duarte Alves Ribeiro for outstanding research assistance. This research was funded by grants UID/GES/00407/2013 and PTDC/IIM-FIN/2977/2014 of the Portuguese Foundation for Science and Technology-FCT. 1. Introduction Rare events, such as the 2007-2009 global financial crisis, are crucial in asset pricing. Rietz (1988) introduces a disaster-risk-based model to explain the equity premium puzzle. In the subsequent literature, Barro (2006) broadens this model to several countries, and Wachter (2013) shows that investors’ perceptions of risk change when rare events occur. If all these models display large conditional equity premia, then the challenge is finding conditional information that best captures this disaster risk and its implied predictability. In general, aggregate-level variables are usually used to predict asset returns. However, seeking and discovering new relations using the non-aggregated quantities of the aggregated phenomenon is intuitive.1 Indeed, if endogenous sectoral shocks hold specific information, they should be used to reflect uncertainty in asset prices. This is even more important when addressing tail comovement, since at the aggregate level tail risk is partially diversified away. Is there a benefit to incorporating endogenous sectoral tail shocks when predicting asset returns? On the one hand, one way to incorporate rare events in finance is to use extreme value theory (e.g., Longin and Solnik 2001, Bae, Karolyi, and Stulz 2003, and Hartmann, Straetmans, and de Vries 2004). For example, Poon, Rockinger, and Tawn (2004) advocate the use of risk measures based on extreme value theory rather than traditional risk measures, such as volatility or value-at-risk. They demonstrate that the latter are unsuitable for measuring tail risk, which may lead to inaccurate portfolio risk assessment. On the other hand, researchers have shown that a powerful solution when examining aggregate-level variables is the use of sectoral information, because different shocks can be recognized at the sectoral level but are invisible at the aggregate level (e.g., Horvath 2000, Veldkamp and Wolfers 2007, Comin and Mulani 2009, and Holly and Petrella 2012). For example, Hong, Torous, and Valkanov (2007) show that industry interdependencies are essential for the predictability of market returns. This paper provides a positive answer to the earlier question. We are the first to analyze the joint effect of tail risk and endogenous sector heterogeneity to predict asset returns. Our first main contribution is to define a new simple and tractable measure of a country’s 1 A more straightforward example can be found in the field of natural sciences, e.g., aggregated behaviors can hide information about non-aggregated pieces, just as studying human cells will give us information that is not perceptible through the study of the human body as a whole. 1 left tail dependency, which has strong and significant predictive power for the U.S. equity premium in-sample (IS) and out-of-sample (OOS). Based on extreme value theory, we first compute the bivariate sectoral tail dependence for each pair of sectors in a country to measure the joint extreme events between the two sectors.2 Then, we compute the average tail dependence between sectors within a country. We designate this average value by the left tail mean, LTM. The main intuition is that existing aggregate market tail measures average out important information about tail risk in the economy, while average tail dependency among sectors conveys this information more precisely. In our setting, out-of-sample equity risk premium (ERP) predictability by the LTM is the result of an optimal hedging strategy3 in which the investor is searching for the “timing” of rare consumption disasters, which have a substantial impact on their equity assets. Investors first observe the aggregate variable; then, a market sectoral joint downturn movement is a strong signal that a systemic event is under way. LTM is a good descriptor of endogenous sectoral tail dependency, and an increase in sectoral tail dependency precedes a disaster. In a setting that assumes no disaster events, a sudden increase of endogenous sectoral tail dependence (LTM increases) will push investors to anticipate a disaster and therefore to rebalance all their positions from equity holdings to other assets (e.g., treasuries) in a typical flight to quality behavior. This process will reinforce the increased value in the observed LTM that will eventually stop either when investors realize they are not in a disaster event or when the disaster occurs with all sectors experiencing a downfall that is not necessarily of the same magnitude across sectors but that has the same starting point. The predictability of a similar “fear” behavior is also observed in Bollerslev, Todorov and Xu (2015). We also compute four other measures of dependence: RTM, CORR, ALTM, and SLTM. The right tail mean, RTM, and the correlation sectors’ mean, CORR, are computed as the LTM but for the joint right tails and joint Pearson correlations, respectively.4 The ALTM is the univariate market tail risk, and the SLTM is the average univariate sectors’ tail risk. We show that the level of the LTM is time- 2 Other authors (e.g., Patton 2009) use Copula functions to model dependence structure. Hilal, Poon, and Tawn (2011) argue that the copula approach imposes conditions on the dependence structure that are too rigid and that the validity of its assumptions was not tested. However, some of the foundations in the extreme value theory are built on the Copula approach, though they impose looser restrictions in the distributions used. 3 In the online appendix, an asset management exercise is provided with the optimal hedging strategy of an investor that consider the existence of rare disasters, and that measures tail dependence with LTM. 4 The CORR intrinsically assumes normality of the truncated distribution of returns. 2 varying, quite adaptive, and it dominates the levels of the RTM, CORR, ALTM, and SLTM through time. It also reacts quickly and more strongly than the other measures. This is evidence that (1) returns in the tails are not drawn from a normal distribution, (2) the tails are asymmetric, and (3) it is important to study the link between the sectors rather than only the risk of each sector or only the overall market.5 A long dispute about the predictability of several common variables (e.g., Campbell and Thompson 2008, Goyal and Welch 2008, Rapach et al. 2010, Ferreira and Santa-Clara 2011, and Li et al. 2015) has persisted. We participate in this debate. We run predictive regressions as in Goyal and Welch (2008). Using a comprehensive set of common variables, we show that there are only two predictors that offer both in- and out-of-sample significant, higher predictive power than the historical average of the equity premium. These two predictors are the LTM and the variance risk premium. Their static and time-varying performances are similar, although their unconditional correlation is quite low, 0.04, indicating a different but valuable impact of these two predictors. We select the new proposed dependence variables as predictors alongside the usual variables, including the short interest index, the variance risk premium, the dividend-price ratio, and the detrended Treasury bill rate. Although the short interest index has in-sample predictability, it clearly fails out-of-sample. We also show that ERP predictability from LTM is due to the sectors’ joint shocks. There is no such predictability in the univariate left tail risk of the aggregate market or in the average of the univariate left tail risk of individual sectors. In fact, using fewer sectors to compute LTM results in lower predictability. We also present evidence that not all sectors and their left tail joint dependencies are related to future risks in the same way. Nevertheless, using a value-weighted average in LTM by the size of each sector leads to the same qualitative conclusions. All these results support our view that the interdependencies of joint left tail sector shocks are an important source of predictability.
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